Theorems · Definition · ring theory
Algebra.TensorProduct.lmulEquiv
(R : Type uR) →
(S : Type uS) →
[inst : CommSemiring R] →
[inst_1 : CommSemiring S] →
[inst_2 : Algebra R S] → [TensorProduct.CompatibleSMul R S S S] → TensorProduct R S S ≃ₐ[S] SIf multiplication by elements of S can switch between the two factors of S ⊗[R] S,
then lmul'' is an isomorphism.
- Defined in
- Mathlib.RingTheory.TensorProduct.Maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- TensorProductstatement · cited by 2,545
- AlgEquivstatement · cited by 1,681
- Algebra.TensorProduct.includeLeftproof · cited by 72
- TensorProduct.CompatibleSMulstatement and proof · cited by 17
- AlgEquiv.ofAlgHomproof · cited by 13
- Algebra.TensorProduct.lmul''proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.mul'_bijective_of_surjectiveproof · cited by 1
- Algebra.TensorProduct.lmulEquiv_eq_lidOfCompatibleSMulstatement and proof · cited by 0
- IsLocalization.bijective_linearMap_mul'proof · cited by 0